منابع مشابه
On Multiple Eigenvalues of Trees
Let T be a tree of order n > 6 with μ as a positive eigenvalue of multiplicity k. Star complements are used to show that (i) if k > n/3 then μ = 1, (ii) if μ = 1 then, without restriction on k, T has k+ 1 pendant edges that form an induced matching. The results are used to identify the trees with a non-zero eigenvalue of maximum possible multiplicity.
متن کاملMultiple Eigenvalues
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each corresponding codimension is the number of conditions which a matrix of the given type must satisfy in order to have the specified multiplicities.
متن کاملOn the kth Eigenvalues of Trees with Perfect Matchings
Let T + 2p be the set of all trees on 2p (p ≥ 1) vertices with perfect matchings. In this paper, we prove that for any tree T in T + 2p , the kth largest eigenvalue λk(T ) satisfies λk(T ) ≤ 1 2 “q ̊ p k ˇ − 1 + q ̊ p k ˇ + 3 ” (k = 1, 2, . . . , p). This upper bound is known to be best possible when k = 1. The set of trees obtained from a tree on p vertices by joining a pendent vertex to each ve...
متن کاملNote on edge-disjoint spanning trees and eigenvalues
Article history: Received 8 December 2013 Accepted 31 May 2014 Available online xxxx Submitted by R. Brualdi MSC: 05C50 15A18 15A42
متن کاملEdge-disjoint spanning trees and eigenvalues
Article history: Received 17 July 2013 Accepted 25 November 2013 Available online 13 December 2013 Submitted by R. Brualdi MSC: 05C50 15A18 15A42
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.01.003